Theory of transformation plasticity

Transformation Plasticity Provides Insights into Concurrent Phase Transformation and Stress Relaxation Observed during Electrochemical Li Alloying of Sn Thin Film

“…In contrast to the literature, where the expression for ε t is based on the unit cell volume of the β phase ( V β ), the present work uses V β* , which is given by The additional term in the right-hand side of eq corresponds to the volume of the Li ions diffused into the active material until the beginning of phase transformation at time t = t *. The choice of V β* instead of V β is mainly due to the following two reasons: First, in true sense, it is the β phase in the presence of diffused Li which undergoes phase change as opposed to the pure β phase. Second, the transformation plasticity strain, − as presented a little later, assumes a constant volume for the transforming phase; while in the present work, the volume of the transforming β phase undergoes significant volume change due to Li diffusion. In the situation where part of the β phase gets yielded before the phase transformation gets initiated and the newer phase α has greater yield strength as compared to the parent phase, the plastic strain ε fβ p ( x , t ) = (ε 1 ( t *) + κ­( t *) x – Ω β C β ( x , t *)/3 + Y β / E fβ ) ( x i ( t ) ≤ h ( t *) ≤ x ≤ ) incurred in the β phase region at the instant of phase transformation ( t = t *) needs to be accounted for in eq while evaluating the stress σ fα ( x , t ) at the same point, but as part of the transformed material α.…”

“…Second, the transformation plasticity strain, − as presented a little later, assumes a constant volume for the transforming phase; while in the present work, the volume of the transforming β phase undergoes significant volume change due to Li diffusion.…”

“…Applying Hooke’s law, the normal component of stress in the α phase σ fα in the x - or z -direction is given by where E fα , Ω α , and ε t are the elastic modulus, partial molar volume of lithium in the α-phase, and transformation strain, respectively. The transformation strain ε t induced in the α phase due to phase transformation has been quantified mainly with respect to two contributions, viz., Eigen strain , and transformation plasticity. − ,, Eigen strain, here also referred to as volumetric mismatch strain, arises due to change in lattice volume in the two phases under consideration, viz., β and α. Thus, the Eigen strain is given as where V α is the unit cell volume of the α phase and V β* corresponds to the unit cell volume of the β phase, having lithium ions inserted at the instant of phase change.…”

“…Accordingly, the present work proposes the mechanism of transformation-induced plasticity (or TRIP) − ,− to be operational in such situations, as above. Transformation plasticity was originally developed by Leblond and co-workers to explain the anomalous plastic behavior during phase transformation in steels undergoing heat treatment when the stress in the system is much lower than the yield stress of the original and the transforming phase.…”

“…In this context, a mathematical model is developed in the present work, which accounts for and develops correlation between elastic–plastic deformation, phase transformation, coupled stress, and electrochemical potential to calculate stresses in thin-film electrodes during electrochemical Li alloying. In addition to using concepts related to Eigen stress, for the first time, the present work introduces the concept of transformation-induced plasticity (i.e., TRIP) − to the electrochemical alloying process. It must be mentioned here that TRIP has traditionally been used for explaining yielding in metallic materials undergoing phase transformation during heat treatment subjected to fairly low (or even nonexistent) average external stresses.…”